Stability of peripheral milling operations with long end mills

This paper presents dynamic modelling of peripheral milling systems with axially varying dynamics. The end mill is divided into differential elements along the cutter axis, and discrete nodes are assigned along the axial depth of cut. The cutting forces, which include regenerative and process damping components, are distributed to nodes. The equation of motion is transformed into modal space as periodic, delayed differential equations which cover one tooth period for regular, and one spindle period for variable pitch cutters. The directional coefficients are averaged and the stability is solved in frequency domain using Nyquist criterion. The presented model is experimentally verified in peripheral milling tests with low radial and high axial depth of cut.